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Search: id:A005436
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| A005436 |
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Number of convex polygons of length 2n on square lattice.
(Formerly M1778)
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+0
6
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| 1, 2, 7, 28, 120, 528, 2344, 10416, 46160, 203680, 894312, 3907056, 16986352, 73512288, 316786960, 1359763168, 5815457184, 24788842304, 105340982248, 446389242480, 1886695382192, 7955156287456, 33468262290096
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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a(n) = number of convex polyominoes of perimeter 2n. - David Callan (callan(AT)stat.wisc.edu), Jul 25 2008
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REFERENCES
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A. Bernini, F. Disanto, R. Pinzani and S. Rinaldi, Permutations defining convex permutominoes, preprint, 2007.
M.-P. Delest and G. Viennot, Algebraic languages and polyominoes enumeration, Theoretical Computer Sci., 34 (1984), 169-206.
A. J. Guttmann and I. G. Enting, The number of convex polygons on the square and honeycomb lattices, J. Phys. A 21 (1988), L467-L474.
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LINKS
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I. Jensen, Table of n, a(n) for n = 2..105 (from link below)
I. Jensen, More terms
Eric Weisstein's World of Mathematics, Convex Polyomino
E. Duchi, S. Rinaldi, and G. Schaeffer, The number of Z-convex polyominoes
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FORMULA
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a(n) = (2*n+11)*4^n -4*(2*n+1)*C(2*n, n).
G.f. x^2*(1-6*x+11*x^2-4*x^3)/(1-4*x)^2-4*x^4*(1-4*x)^(-3/2). - Markus Voege (voege(AT)blagny.inria.fr), Nov 28 2003
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CROSSREFS
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a(n) = A005768(n) + A005769(n) + A005770(n).
Adjacent sequences: A005433 A005434 A005435 this_sequence A005437 A005438 A005439
Sequence in context: A116078 A090317 A130655 this_sequence A026770 A010683 A005435
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe, njas
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